Sundman Transformation Pair for force-free Duffing-van der Pol oscillator by using Algorithm

Ozlem Orhan¹ Bahar Milani² Muhammed Milani³

1) Assistant Professor Bandirma University, Faculty of Basic Engineering - Bandirma, Turkey,
2) Assistant Professor Bandirma University, Faculty of computer Engineering - Bandirma, Turkey,
3) Assistant Professor Bandirma University, Faculty of computer Engineering - Bandirma, Turkey,

Publication : 2nd. International Congress on science & Engineering - paris(parisconf.com)
Abstract :
It is shown that the force-free Duffing-van der Pol oscillator is integrable for a specific nonlinear term in this study. Firstly, force-free Duffing-van der Pol oscillator is classified using special functions. Then, a useful algorithm is emphasized to obtain Sundman transformation pair. At the end of this classification, the Sundman transformation pair is obtained by using this useful algorithm. After obtaining Sundman transformation pair the first integral of the equation is yield. Therefore, the first integral of force-free Duffing-van der Pol oscillator is found. It is examined the dynamical behaviour of the oscillator equation. Therefore, the nonlinear terms which have rich dynamics and can have important applications in secure communications, random number generations, cryptography, and the other similar areas.
Keywords : Sundman transformation pair Useful Algorithm Differential equations First Integral Duffing-Van der Pol Oscillator equation.